9.3 - Lesson 9 Summary

Objectives

Upon successful completion of this lesson, you should be able to:

  • Identify situations in which the z or t distribution may be used to approximate a sampling distribution
  • Construct a confidence interval to estimate the difference in two population proportions and two population means using Minitab Express given summary or raw data
  • Conduct a hypothesis test for two proportions and two means using Minitab Express given summary or raw data
  Confidence Interval Test Statistic
Two Independent Proportions
At least 10 successes and 10 failures in both samples.
\((\widehat{p}_1-\widehat{p}_2) \pm z^\ast {\sqrt{\frac{\widehat{p}_1 (1-\widehat{p}_1)}{n_1}+\frac{\widehat{p}_2 (1-\widehat{p}_2)}{n_2}}}\) \(z=\frac{\widehat{p}_1-\widehat{p}_2}{\sqrt{\widehat{p}(1-\widehat{p})\left ( \frac{1}{n_1}+\frac{1}{n_2} \right )}}\)
Two Independent Means
Both sample size are at least 30 OR populations are normally distributed.

\((\bar{x}_1-\bar{x}_2) \pm t^\ast{ \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}\)

\(Estimated \;df = smallest\; n - 1\)

\(t=\frac{\bar{x}_1-\bar{x}_2}{ \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}\)

\(Estimated \;df = smallest\; n - 1\)